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Consisten YEC Cosmology Consistent YEC Cosmology P.W. Dennis Outline • Introduction. The “problem” and roadmap to solution • Philosophies of Time – Eternalism (“Time is a place”) vs. Presentism (“Time is not a place”). – Relativistic paradoxes. Rethinking “simultaneity.” • General Relativistic Solution – Time paradoxes in cosmological solutions – Cut and Stitch Approach. Specifying initial conditions. – FLRW solution, inhomogeneous models. – YEC solution. Initial Conditions. • Discussion and Conclusions The “Problem” • Given that the universe is only 6000 years old, no object further than ~6000 light years would be observable today. – Diameter of the observed universe is widely considered to be 92 billion light years – Minkowskian (“flat” with no gravity, the space-time of SR) universe would seem to imply a universe of tens of billion years old. – Calculation using exact GR calculation in expanding cosmos gives ~14 Gyrs. – Note: GR does not prohibit a global faster than light expansion of space. Only local speed of light is constant. • Cornerstones of Solution • Biblical Philosophical view of time – “presentism” • Sound General Relativistic Principles, Methods and Interpretation • Geometry of null geodesics (light rays) • Choice of initial conditions, i.e. spatial hypersurface at the moment of creation. Roadmap to Solution (1 of 3) • Goal: Looking for general Space like surface Time b t (now) relativistic solution for small light a arrival time • Light rays are null geodesics • Solution within GR must be based on the geometry of null geodesics Space like and spacelike surfaces surface • Important point: GR does not t provide a prescription for a b specifying a spacelike surface at Local light cone space moment of creation Roadmap to Solution (2 of 3) • The constraints of a young earth, Space like surface distant galaxies and the physics of GR Time t b (now) require the YEC solution to respect a null geodesics and have a special Small creation surface (initial conditions) to time null geodesics achieve small time at earth. o n Large • Note: If t is a surface of time space like homogeneous matter density, then surface at creation 0 0 is a surface of inhomogeneity. moment • is space like since surface normal t ao b is time like everywhere: space g( n , n ) 0 Local light cone • Point set of solution manifold excludes points below Roadmap to Solution (3 of 3) Space like surface • Ingredients that a consistent YEC cosmology can use. Time b t (now) a – Geometry of null geodesics Small – Choice of parameterized creation time null geodesics spacelike surface o n – “cut and stitch” approach in GR Large – Inhomogeneous solutions time space like surface • Using these, many particular solutions at creation 0 are possible consistent with the Bible. moment t ao b space Local light cone The Problem INTRODUCTION Time is not a place! PHILOSOPHIES OF TIME Eternalism vs. Presentism Eternalism in a Nutshell • “Eternalism” is the philosophy that time is an illusion. – Past, present and future events (referred to via tensed verbs) are eternally existing in a universe in which time has been “spatialized.” – It is a universe in which there is no “now” – no unique “present.” – It is sometimes called a “block-house” universe in which nothing really happens. – Slogan: “Time is a place” • Was the view of Einstein, Weyl and others, such as the Idealists • Theories of relativity seemed to support this view • Minkowski’s formulation of events located in a 4D spacetime lent credence to the spatialization of time Einstein’s Eternalism – "The four-dimensional continuum is now no longer resolvable objectively into sections, which contain all simultaneous events; “now” loses for the spatially extended world its objective meaning. It is because of this that space and time must be regarded as a four-dimensional continuum that is objectively unresolvable." A. Einstein. – “People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.” A. Einstein. Structure of Space-time t =− t vx/ c2 Time ( ) 2 2 2 2 2 2 • Minkowski’s mathematical formulation ds= dx + dy + dz − cdt x' =− ( x vt) represents space & time as a 4D continuum 2 Time like Future ds 0 of events (t,x,y,z) • Basis of eternalist claim. Lorentz transform Future Null Cone (LT) mixes time and space. Theory moves 2 A ds = 0 from time & 3-vectors to 4-vectors. 2 • Invariance under Poincaré group rather than Space like ds 0 Space Galilean transformations. E • The interval is a LT invariant. A geometric property independent of coordinate charts. – Time like regions are causally connected. Past Null Cone – Space like regions are causally independent Time like Past • Relativity operationally no knowledge of simultaneity in the space like regions. Theological & Philosophical Defects of Eternalism • Eternalism prima facie makes creatures coeternal with God. As Christians we thus reject it. • Weyl (1949): “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along the lifeline of my body, does a section of the world come to life as a fleeting image in space which continually changes in time.” (emphasis added) • Note the incoherence. Nothing happens in the world yet there are changes. • Philosophically, to account for temporal experience, the eternalist must replace a single flow of time with myriads of subjective time flows. Hardly a cogent philosophical position. Presentism • “Presentism” is the contrary view that the present is real • The creation is not a Parmenidean block house universe • There is an actual real moment called “now” throughout the cosmos • The present continually passes. The past is forever gone, the future will be. • Contrary to many opinions, presentism is compatible with relativistic physics – Eddington and Reichenbach correctly point out relativity is neutral to passage of time. • Arguments to the contrary are philosophically flawed (as above) or misuse the assumptions and mathematics of relativity – Eternalist interpretation is due to endowing an epistemological conclusion (inability to operationally detect simultaneity) with a metaphysical conclusion (time is not real). – But, inability to operationally detect simultaneity does not imply time is not real. Relativistic paradoxes. Rethinking “simultaneity.” t = 0 t =t0 ). =constant must be “real to you. An Eternalist Argument • Consider two observers, “me” and “you.” You are moving in the negative direction relative to me. • Lorentz transformation implies “my now” (t) differs from “your now” (t’). • Events with t=constant are “real” to me . Events with t’ =constant are “real” to you. • You and me are “real” to each other at t=t’=0. • By transitivity: – all events in “your now” are real to you. – you are real to me at t=0 – events in “my now” are real to me, then – all events in “your now” are equally real to you, and therefore, also real to me and to all the events in “my now.” Thus, “my now” and “your now” are equally real • All events, past, present and future, are equally “real” to you and me, and equally real for all observers. Thus, time is an illusion. t = 0 t =t0 ). =constant must be “real to you. Eternalist Argument Conclusion • Observers only see events causally connected to the current time by way of the past null cone. – Entire t=constant surface is never actually observed! • Different time labels for a space-time event in no way proves there is not a real present. – Only implies that an objective “now” is not determinable for us – not that it does not exist! • Proper time of observers is not an exact differential. – Operationally extending local proper time as a global time coordinate is necessarily observer dependent – Has no metaphysical bearing on presentism. • Extension of proper time off of a time line is only a mathematical procedure for labeling space-time events. – Defining t=0 or t’=0 as “simultaneous” is only a convention • Asserting that a constant time spacelike surface (according to the LT) is “real” begs the question! X − instantaneously jumped back into the past due to the acceleration of the observer at event O Acceleration: Counterexample to “Simultaneity” Arguments • Coordinates are merely labels and have no necessary metaphysical connection to simultaneity or the reality of events! • Naïve extension of Lorentz coordinates leads to bizarre action at a distance effects – Future event E in X+ instantaneously jumps into the past due to the acceleration. – Some events in X+ are no longer simultaneous with O. O • Note: X+ and X- are causally independent of O! • Construction has ignored Einstein’s operational procedure for time coordinates. • Correct method: use radar ranging (outlined in proceedings) • Bottom line: By relativistic principles “simultaneity” is not an observable! Time is not a place! GENERAL RELATIVISTIC SOLUTION Time paradoxes in cosmological solutions = − to= . Example: The “Eternal” Black Hole Universe • Plotted in Kruskal-Szekeres coordinates • Solid lines are Schwarzschild “time” t • Dashed lines are Schwarzschild “radius” r • “Eternal” since observer who maintains a constant radial distance greater than r = 2M (region I) has infinite time extent • An observer at X = 0 falling from r = 0 in region IV to r = 0 in region II has a finite history! Schwarzschild Spacelike Surfaces • Surfaces of simultaneity. By relativistic principles any surface could be taken as an actual surface representing the present “now.” • Surfaces temporally ordered: AA’ earlier than BB’ etc. • Presentism and Christian theism implies one such spatial hypersurface must be “now” (not by convention). • Infinite past is inconsistent with Christian theism. • Infinite past is a mathematical fiction • There is an initial hypersurface = “the time of creation.” For example, BB’. The solution below BB’ is to be cut out and discarded. “Cut and Stitch” solution. Cut and Stitch Approach. Specifying initial conditions. Example: Stitching Together Two Friedmann-LeMaitre- Robertson-Walker (FLRW) Models • Diagram of two FLRW regions connected via a vacuum neck. • “Big Bangs” and the “Big Crunches” are non-simultaneous.
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